function [J grad] = nnCostFunction(nn_params, ...
                                   input_layer_size, ...
                                   hidden_layer_size, ...
                                   num_labels, ...
                                   X, y, lambda)
%NNCOSTFUNCTION Implements the neural network cost function for a two layer
%neural network which performs classification
%   [J grad] = NNCOSTFUNCTON(nn_params, hidden_layer_size, num_labels, ...
%   X, y, lambda) computes the cost and gradient of the neural network. The
%   parameters for the neural network are "unrolled" into the vector
%   nn_params and need to be converted back into the weight matrices. 
% 
%   The returned parameter grad should be a "unrolled" vector of the
%   partial derivatives of the neural network.
%

% Reshape nn_params back into the parameters Theta1 and Theta2, the weight matrices
% for our 2 layer neural network
Theta1 = reshape(nn_params(1:hidden_layer_size * (input_layer_size + 1)), ...
                 hidden_layer_size, (input_layer_size + 1));

Theta2 = reshape(nn_params((1 + (hidden_layer_size * (input_layer_size + 1))):end), ...
                 num_labels, (hidden_layer_size + 1));

% Setup some useful variables
m = size(X, 1);
         
% You need to return the following variables correctly 
J = 0;
Theta1_grad = zeros(size(Theta1));
Theta2_grad = zeros(size(Theta2));

% ====================== YOUR CODE HERE ======================
% Instructions: You should complete the code by working through the
%               following parts.
%
% Part 1: Feedforward the neural network and return the cost in the
%         variable J. After implementing Part 1, you can verify that your
%         cost function computation is correct by verifying the cost
%         computed in ex4.m
%
% Part 2: Implement the backpropagation algorithm to compute the gradients
%         Theta1_grad and Theta2_grad. You should return the partial derivatives of
%         the cost function with respect to Theta1 and Theta2 in Theta1_grad and
%         Theta2_grad, respectively. After implementing Part 2, you can check
%         that your implementation is correct by running checkNNGradients
%
%         Note: The vector y passed into the function is a vector of labels
%               containing values from 1..K. You need to map this vector into a 
%               binary vector of 1's and 0's to be used with the neural network
%               cost function.
%
%         Hint: We recommend implementing backpropagation using a for-loop
%               over the training examples if you are implementing it for the 
%               first time.
%
% Part 3: Implement regularization with the cost function and gradients.
%
%         Hint: You can implement this around the code for
%               backpropagation. That is, you can compute the gradients for
%               the regularization separately and then add them to Theta1_grad
%               and Theta2_grad from Part 2.
%

X_ones=ones(m,1);
X_f=[X_ones X];
Final_Delta_2=zeros(size(Theta2));
Final_Delta_1=zeros(size(Theta1));
for i=1:m
    %Cost Function
    Real_output=zeros(num_labels,1);
    Real_output(y(i))=1;
    Z_2=Theta1*(X_f(i,:))';
    Layer2= sigmoid(Z_2);
    Layer2_bias=[1; Layer2];
    Z_3=Theta2*Layer2_bias;
    H_theta=sigmoid(Z_3);
    Cost_i=sum(-Real_output.*log(H_theta)-(1-Real_output).*log(1-H_theta));
    J=J+Cost_i;
    %Gradient
    %a_1=(X_f(i,:))' and a_2=Layer2_bias
    Delta_3=H_theta-Real_output;
    Theta_2_temp=Theta2(:,2:end);
    Delta_2=((Theta_2_temp)'*Delta_3).*sigmoidGradient(Z_2);
    
    Final_Delta_2=Final_Delta_2+Delta_3*((Layer2_bias)');
    
    Final_Delta_1=Final_Delta_1+Delta_2*(X_f(i,:));
    
end



Theta1_temp=Theta1(:,2:end);
Theta2_temp=Theta2(:,2:end);

Theta1_temp=Theta1_temp.^2;
Theta2_temp=Theta2_temp.^2;

Reg_cost=lambda*(sum(Theta1_temp(:))+sum(Theta2_temp(:)))/(2*m);


Theta1_grad=(Final_Delta_1/m)+[zeros(size(Theta1_grad,1),1) (lambda/m)*Theta1(:,2:end)];
Theta2_grad=(Final_Delta_2/m)+[zeros(size(Theta2_grad,1),1) (lambda/m)*Theta2(:,2:end)];



J=J/m; 

J=J+Reg_cost;













% -------------------------------------------------------------

% =========================================================================

% Unroll gradients
grad = [Theta1_grad(:) ; Theta2_grad(:)];

end
